Journal of the Mathematical Society of Japan

Reduction of generalized Calabi-Yau structures

Yasufumi NITTA

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Abstract

A generalized Calabi-Yau structure is a geometrical structure on a manifold which generalizes both the concept of the Calabi-Yau structure and that of the symplectic one. In view of a result of Lin and Tolman in generalized complex cases, we introduce in this paper the notion of a generalized moment map for a compact Lie group action on a generalized Calabi-Yau manifold and construct a reduced generalized Calabi-Yau structure on the reduced space. As an application, we show some relationship between generalized moment maps and the Bergman kernels, and prove the Duistermaat-Heckman formula for a torus action on a generalized Calabi-Yau manifold.

Article information

Source
J. Math. Soc. Japan, Volume 59, Number 4 (2007), 1179-1198.

Dates
First available in Project Euclid: 10 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1197320632

Digital Object Identifier
doi:10.2969/jmsj/05941179

Mathematical Reviews number (MathSciNet)
MR2370010

Zentralblatt MATH identifier
1186.37064

Subjects
Primary: 37J15: Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]
Secondary: 14J32: Calabi-Yau manifolds

Keywords
generalized Calabi-Yau structures moment maps Bergman kernels the Duistermaat-Heckman formula

Citation

NITTA, Yasufumi. Reduction of generalized Calabi-Yau structures. J. Math. Soc. Japan 59 (2007), no. 4, 1179--1198. doi:10.2969/jmsj/05941179. https://projecteuclid.org/euclid.jmsj/1197320632


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References

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